





'''simple docstring'''


from __future__ import annotations

from fractions import Fraction


def 						__a(SCREAMING_SNAKE_CASE_	:       int		,							SCREAMING_SNAKE_CASE_	:       int     ):



    '''simple docstring'''





    return (
        num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
    )


def 						__a(SCREAMING_SNAKE_CASE_	:       int     ):



    '''simple docstring'''





    _lowerCAmelCase						      =   []
    _lowerCAmelCase						      =   11
    _lowerCAmelCase						      =   int("1" + "0" * digit_len     )
    for num in range(SCREAMING_SNAKE_CASE_		,							SCREAMING_SNAKE_CASE_     ):
        while den <= 99:
            if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
                if is_digit_cancelling(SCREAMING_SNAKE_CASE_		,							SCREAMING_SNAKE_CASE_     ):
                    solutions.append(F'''{num}/{den}'''     )
            den += 1
        num += 1
        _lowerCAmelCase						      =   10
    return solutions


def 						__a(SCREAMING_SNAKE_CASE_	:       int = 2     ):



    '''simple docstring'''





    _lowerCAmelCase						      =   1.0
    for fraction in fraction_list(SCREAMING_SNAKE_CASE_     ):
        _lowerCAmelCase						      =   Fraction(SCREAMING_SNAKE_CASE_     )
        result *= frac.denominator / frac.numerator
    return int(SCREAMING_SNAKE_CASE_     )


if __name__ == "__main__":
       print(solution())




"""simple docstring"""






import warnings

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding



class 			lowercase					( lowercase__		):
			lowercase        =     ['''image_processor''', '''tokenizer''']
			lowercase        =     '''CLIPImageProcessor'''
			lowercase        =     ('''XLMRobertaTokenizer''', '''XLMRobertaTokenizerFast''')






			def __init__(self  :	Union[str, Any]      ,SCREAMING_SNAKE_CASE_  :	int=None      ,SCREAMING_SNAKE_CASE_  :	str=None      ,**SCREAMING_SNAKE_CASE_  :	Union[str, Any]			)       ->	int:





				"""simple docstring"""


				lowerCAmelCase												=  None
				if "feature_extractor" in kwargs:
					warnings.warn(
					    '''The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`'''
					    ''' instead.'''      ,SCREAMING_SNAKE_CASE_      ,)
					lowerCAmelCase												=  kwargs.pop('''feature_extractor'''			)

				lowerCAmelCase												=  image_processor if image_processor is not None else feature_extractor
				if image_processor is None:
					raise ValueError('''You need to specify an `image_processor`.'''			)
				if tokenizer is None:
					raise ValueError('''You need to specify a `tokenizer`.'''			)

				super().__init__(SCREAMING_SNAKE_CASE_      ,SCREAMING_SNAKE_CASE_			)






			def __call__(self  :	Union[str, Any]      ,SCREAMING_SNAKE_CASE_  :	List[str]=None      ,SCREAMING_SNAKE_CASE_  :	Optional[int]=None      ,SCREAMING_SNAKE_CASE_  :	Union[str, Any]=None      ,**SCREAMING_SNAKE_CASE_  :	Any			)       ->	List[Any]:





				"""simple docstring"""


				if text is None and images is None:
					raise ValueError('''You have to specify either text or images. Both cannot be none.'''			)

				if text is not None:
					lowerCAmelCase												=  self.tokenizer(SCREAMING_SNAKE_CASE_      ,return_tensors=SCREAMING_SNAKE_CASE_      ,**SCREAMING_SNAKE_CASE_			)

				if images is not None:
					lowerCAmelCase												=  self.image_processor(SCREAMING_SNAKE_CASE_      ,return_tensors=SCREAMING_SNAKE_CASE_      ,**SCREAMING_SNAKE_CASE_			)

				if text is not None and images is not None:
					lowerCAmelCase												=  image_features.pixel_values
					return encoding
				elif text is not None:
					return encoding
				else:
					return BatchEncoding(data=dict(**SCREAMING_SNAKE_CASE_			)      ,tensor_type=SCREAMING_SNAKE_CASE_			)






			def 					UpperCAmelCase							(self  :	List[str]      ,*SCREAMING_SNAKE_CASE_  :	Union[str, Any]      ,**SCREAMING_SNAKE_CASE_  :	Tuple			)       ->	Optional[Any]:





				"""simple docstring"""


				return self.tokenizer.batch_decode(*SCREAMING_SNAKE_CASE_      ,**SCREAMING_SNAKE_CASE_			)






			def 					UpperCAmelCase							(self  :	Union[str, Any]      ,*SCREAMING_SNAKE_CASE_  :	int      ,**SCREAMING_SNAKE_CASE_  :	Union[str, Any]			)       ->	Any:





				"""simple docstring"""


				return self.tokenizer.decode(*SCREAMING_SNAKE_CASE_      ,**SCREAMING_SNAKE_CASE_			)






			@property
			def 					UpperCAmelCase							(self  :	List[Any]			)       ->	Dict:





				"""simple docstring"""


				lowerCAmelCase												=  self.tokenizer.model_input_names
				lowerCAmelCase												=  self.image_processor.model_input_names
				return list(dict.fromkeys(tokenizer_input_names + image_processor_input_names			)			)


